Finite Group Databasebeta

C2×#30684103 #46800643

order33952
automorphism?
homologyAbelianization (H1) = C23 · Schur multiplier (H2) = C22

Aliases

direct productC2×#30684103

Splittings

FittingC2×Q8×C1061 ⋊ C2
SylowC1061 ⋊ C2×SD16

Subgroups

subgroupG/H
centerC22C22⋊D1061
commutator, cosocleC4×C1061C23
FrattiniC4C22×D1061
FittingC2×Q8×C1061C2
socleC22×C1061D4
prime radicalC2×D4244C2
hypercenterC2×Q8D1061
hypocenterC1061C2×SD16
LCSG ▷ C4×C1061 ▷ C2×C1061 ▷ C1061
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×Q8

68 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 16976

Conjugacy classes & character table

5314 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33952, 159);